What is Bose-einstein: Definition and 79 Discussions
In condensed matter physics, a Bose–Einstein condensate (BEC) is a state of matter (also called the fifth state of matter) which is typically formed when a gas of bosons at low densities is cooled to temperatures very close to absolute zero (−273.15 °C or −459.67 °F). Under such conditions, a large fraction of bosons occupy the lowest quantum state, at which point microscopic quantum mechanical phenomena, particularly wavefunction interference, become apparent macroscopically. A BEC is formed by cooling a gas of extremely low density (about one-hundred-thousandth (1/100,000) the density of normal air) to ultra-low temperatures.
This state was first predicted, generally, in 1924–1925 by Albert Einstein following and crediting a pioneering paper by Satyendra Nath Bose on the new field now known as quantum statistics.
When various atoms are turned into BEC's, are their electrons still arranged in their standard atomic orbitals like at higher temperatures? Or are the electrons free floating around the entire condensate? If the electrons are free-floating, then are they arranging themselves into superconductive...
Want to integrate the total energy density over all photon energies between two
temperature values from 500K to 5800K, but not sure how to proceed.
Here is some examples to help:
Einstein condensate state or ultra hot fully ionized, removed of all-electron, plasma that is compressed like possibly something like fusion, state (an extraordinarily unattainable state currently; like compressed air into a liquid, but a solid; while even metallic hydrogen is, as far as I know...
I have seen many of these diagrams in internet and I fail to figure out what their actual meaning is. Can someone explain what the axes and different colours mean? Also, which is the physical interpretation that can be extracted from them? Thanks in advance :).
iam not getting why in bose statistics the number of ways to arrange ni particles in gi degenerate states is = (gi+ni-1) ?
and why do we divide by ni factorial , and gi factorial .
In the book A Quantum Approach to Condensed Matter Physics by Taylor and Heinonen they write the following passage on page 87:
Now I don't understand what does it mean "macroscopic number", how many particles?
I am studyng the deduction of Fermi-Dirac and Bose-Einstein distribution, but I'm not understanding one part. If we have a system of ##N## identical non-interaction particles, with energies levels ##\varepsilon _{l}## and occupation number ##n_{l}## (this is the number of particles with the same...
https://www.livescience.com/10288-kind-light-created-physics-breakthrough.html
I was reading here that you can freeze photons.
What does it mean to freeze up a photon, are you slowing down it's motion, changing it's energy levels. Or are you changing the state of the particles around it and...
Homework Statement
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I have solve the rest of this problem pretty easily and see no problems with working with Indistinguishable particles, Distinguishable particles, fermions and Bosons. Part c has me very confused though about what it is even asking.
Suppose a system with equally spaced...
Hello,
I have a question regarding the derivation for Bose Einstein condensation. I understand that in a boson gas for high temperatures the expectation value of the total number of particles should equal something like: $$ \langle N \rangle \sim T * \eta(z)$$ With ## z = exp(\frac {\mu} {k_b...
Homework Statement
The actual question was deriving Bose-Einstein, but I got confused on the F-D example. I'm basically following the method given here.
Homework Equations
[All taken directly from the above link]
Taylor series:
The Attempt at a Solution
So after that third equation...
I'm not a physicist nor an academic, however, the world around me fascinates me. I was watching YouTube and came across an explanation of Bose Einstein condensate, and thought with less space between atoms that would potentially be a better target for creating new elements. So my question is...
I was wondering, if cooled sodium or rubidium atoms behave as bosons, can they also occupy the same space?
I tried to google a bit, but as usual, articles throw letters like ##\beta##, ##s##, ##\lambda##, ##g## around without bothering to at least give them a name so I could search deeper. I...
Hello forum! I'm studying classical and quantum coherence and there's some bug in particular I can't solve on my own, nor I could find anywhere.
I've read that a Bose-Einstein condensate is a coherent state but it seems to me inconsistent with the definition of coherence given by Glauber. In...
This paper https://arxiv.org/abs/quant-ph/9911101 says this:
If we normalize those terms, don't we get 1/4 , 1/2 , 1/4 as the probabilities, since ##|HT\rangle## and ##|TH \rangle## are indistinguishable?
Homework Statement
I'm trying to understand a derivation of the Fermi-Dirac and Bose-Einstein distributions. In my textbook Thermal Physics by D. V. Schroeder it says: "The idea is to first consider a "system" consisting of one single-particle state, rather than a particle itself. Thus the...
When computing the probability distribution of bosons, why is A = 1 for photons? Does this not imply that photons will have an increasingly high probability of being present as E approaches 0? What is the significance of such a situation?
In section 7.1 of his statistical mechanics, Pathria derives the formula ## N_e=V\frac{(2\pi m k T)^{\frac 3 2}}{h^3}g_{\frac 3 2}(z) ## where ## \displaystyle g_{\frac 3 2}(z)=\sum_{l=1}^\infty \frac{z^l}{l^{\frac 3 2}} ## and ## z=e^{\frac \mu {kT}} ##. This formula gives the number of...
So a Bose Einstein condensate is another state of matter at temperatures below those where a solid state exists.
The temperature is reduced so much, that the quantum wave states overlap and become one single object.
So what are the properties of this object? Is it more rigid than solids...
Say I have ##n_{a}## bosons in some state ##a##, then the transition rate from some state ##b## to state ##a##, ##W^{boson}_{b\rightarrow a}##, is enhanced by a factor of ##n_{a}+1## compared to the corresponding transition probability for distinguishable particles, ##W_{b\rightarrow a}##, i.e...
Homework Statement
To study the thermodynamic behavior of the limit $$z\rightarrow1$$ it is useful to get the expansions of $$g_{0}\left( z\right),g_{1}\left( z\right),g_{2}\left( z\right)$$
$$\alpha =-\ln z$$ which is small positive number. From, BE integral,
$$g_{1}\left( \alpha \right)...
Hello
What are some method or references to consider BECs or atom lasers in finite temperatures with Gross-Pitaevskii equation?
There is quantum mechanical approach but I want a mean field approach which considers thermal or quantum noises too.
If possible, introduce some references.
Thank you...
So I have just been reading up on statistical thermodynamics and have no idea why the bose-einstein, fermi dirac and maxwell boltzman are all integers, that makes sense, but then when you make the degenerate correction to the maxwell Boltzmann by dividing by N! we get decimal answers. Why is...
Homework Statement
Hi guys,
I'm having some troubles on a problem. There are N spinless particles with allowed energies ##\vec p^2 /(2m)## and ##-\gamma## where ##\gamma >0##.
1)Find the number of particles with energy ##-\gamma## in function of T.
2)Which conditions must ##\mu## satisfy?
3)Is...
I haven't learned about this yet in school but I'm assuming as the atoms condense down to a single wavelength the volume of the liquid would be very small. If this condensate was instantly released out of a vacuum and into normal atmospheric pressure, would the volume rapidly expand?
Secondly...
Homework Statement
Consider a 2-dimensional Bose-Einstein ideal gas.
1)Calculate the grand partition function of that system.
2)Calculate the mean number of particles per unit area in function of T and z, the fugacity.
3)Show that there's no Bose-Einstein condensate for this system.
Homework...
Homework Statement
I am trying to evuluate the value of the integral:
J= \int_{0}^{∞} \frac{x^{3}}{e^{x}-1}dx
Could you please supply me with the method used for that? I thought of breaking the integral from 0 to 1 and from 1 to infinity. That way I could expand the exponential to taylor...
Homework Statement
Hey guys,
So here's what we have:
Bose-Einstein function
g_{v}(z)=\frac{1}{\Gamma(z)}\int_{0}^{\infty}\frac{x^{v-1}dx}{z^{-1}e^{x}-1}
Fermi function
f_{v}(z)=\frac{1}{\Gamma(z)}\int_{0}^{\infty}\frac{x^{v-1}dx}{z^{-1}e^{x}+1}
And we have the series version of...
I worked out the Planck Black-Body Radiation Formula using Bose-Einstein Statistics, but I feel there is something conceptual I am missing here.
When Planck derived the formula, he started out with the Boltzmann distribution function, and assumed that there were discrete energy levels...
Consider a macroscopic Bose-Einstein condensate. Are there experimental results regarding the propagation (in space and time) of the collapse of this state caused by a point-like perturbation?
Hello!
I have a small question, and I am not sure if I am missing something:
Today I glanced at the wikipedia page for Pions, and saw this: Statistics: Bosonic
Can anyone explain to me why a quark paired with a anti-quark obey Bose-Einstein Statistics? If quarks obey Fermi-Dirac statistics...
Hello guys,
I would really need some help on the following problem.
Consider a non-interacting & non-relativistic bosonic field at finite temperature. We are all aware of the fact that such a statistical system is well described by the grand-canonical ensemble in the limit N→∞. However...
Homework Statement
Variables: N (number of particles), μ (chemical potential), P (pression), V (volume).
k is Boltzmann's constant. I often use β=1/kT.
The (isothermal) compressibility is given by
\kappa_{T} = -\frac{1}{V}\left (\frac{\partial V}{\partial P}\right )_{N,T}
The...
Good afternoon. I am wondering if quantum entanglement could be created between two thermodynamically isolated Bose-Einstein condensates of the same atom produced at the same time in close proximity. Due to the similarity of the systems' mathematics regarding their quantum states (wave...
Homework Statement
Bose-Einstein condensation of a fluid occurs when the de Broglie wavelength of a "typical" particle becomes greater than the average nearest-neighbor distance. One can interpret the momentum in the de Broglie equation as
p=\sqrt{<p^{2}>}
where <p^{2}> means the thermal...
Homework Statement
Estimate the Bose-Einstein condensation temperature of Rb 87 atoms with density of 10^11 atoms per cm^3.
Homework Equations
T=\frac{n^{2/3}h^{2}}{3mK_{B}}
The Attempt at a Solution
This should be just a standard plug and chug question, but my answers are not...
1. Problem From Fitzpatrick we need to deriveln(Z)=αN-\sum ln(1-e^{-\alpha-\betaε_{r}}) (Equation 8.45)
Homework Equations
This is claimed to be derived from Equations 8.20, 8.30, and 8.43
Eq 8.20
\overline{n}_{s}=-\frac{1}{\beta}\frac{\partial ln(Z)}{\partial\epsilon_{s}}
Eq 8.30...
Dear all,
I have been reading Wonders of the Universe by Prof. Brian Cox. I enjoyed the TV programs and thought the book would also be interesting, which it is. In the last chapter of the book, and also discussed in the TV program, it talks about the end of the Universe in many trillions of...
A question occurred to me concerning the Bose-Einstein condensate:
When you have a quantum gas of bosons at a low temperature you obtain a Bose-Einstein condensate where some bosons are in the same state. When you consider the two bosons with the same state, they should behave like one boson...
Homework Statement
Given 4 particles to be divided among 2 zones, one of 3 cells and one of 2 cells. For B-E statistics find W for each macrostate from N1=4, N2=0 to N1=0, N2=4, using both the formula and block diagram.
Homework Equations
The relevant equation is W=(g+Ni-1)!/(g-1)!Ni...
So, I've managed to get the distribution in a decent way. Using this code;
hw = 1;
kt = 25;
n = 10000;
dist[b_] := 1/(b*Exp[hw*m/kt] - 1);
normsum[b_] := Sum[dist[b]*(m + 2)*(m + 1)/2, {m, 0, 300}]
q = FindRoot[normsum[b] == n, {b, 0.5}]
occnumber = Table[N[dist[b /. q]*(m + 2)*(m +...
I'm not absolutely sure whether condensation of ideal gas of bosons (without
any interactions) is a first order phase transition. Some people claim that it
isn't first order phase transition because the entropy of a system is continuous
function at critical temperature. According to me however...
Hey guys,
So I have to make a presentation on this topic. Does anyone of you know of any recent applications of this phenomenon or helpful introductory paper/article? I'm doing my own independent research too but thought that you guys might know of a very helpful resource/idea that I can look...
I was surfing the web and came across where a lab team was messing around with Bose-Einstein Condensate and created what seemed to be a supernova.
Here is the link. http://www.space.com/scienceastronomy/generalscience/supernova_lab_010723.html
Does anyone on have any idea how this might...